#12: If the slope of a linear function is m = 6/5, how much
does the output change, when the input is decreased by 30?
The output changes by:

The length of the model car based on the information is 0.8 feet.

It should be noted that scale simply shows the relationship between a measurement on a model as well as the corresponding measurement on the actual object.

From the information, the model car is constructed with a scale of 1:15.

When the actual car is 12 feet long, the length of the model will be illustrated as x. This will be:

= 1/15 = x / 12

Cross multiply

15x = 1 × 12

15x = 12

Divide

x = 12 / 15

x = 0.8

The length is 0.8 feet.

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a. The scalar projection of b onto a is -6.50

b.  the vector b into a component parallel to a and a component orthogonal to a. Parallel component: (-1.67, 2.77, -5.24) and Orthogonal Component  [9, -5, 1]

(A) The scalar projection of b onto a is given by:

proj_a(b) = (b . a) / ||a||

where "·" denotes the dot product and "|| ||" denotes the norm (magnitude) of a.

So, we have:

b . a = (-3)(9) + (5)(-5) + (-9)(1) = -78

||a|| = √[(-3)^2 + 5^2 + (-9)^2] = √[115]

Therefore:

proj_a(b) = (-78) / √[115] ≈ -6.50

(B) To find the component of b parallel to a, we can use the scalar projection we just found and multiply it by the unit vector in the direction of a. The unit vector in the direction of a is given by:

u_a = a / ||a||

So, we have:

comp_parallel = proj_a(b) * u_a

= (-6.50) * [(-3)/sqrt[115], 5/√[115], (-9)/sqrt[115]]

≈ (-1.67, 2.77, -5.24)

To find the component of b orthogonal to a, we can subtract the parallel component from b:

comp_orthogonal = b - comp_parallel

= [9, -5, 1] - (-1.67, 2.77, -5.24)

≈ (10.67, -7.77, 6.24)

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Answer: C

Step-by-step explanation:

Answer:

X=18

Y=52

Step-by-step explanation:

Let X represent the first type of ticket sold at the concert

Let Y represent the second type of ticket sold at the concert-----equation 1

X + Y= 70 (Total number of tickets sold) ------equation 2

(X×10) + ( Y×12)=$804. ( Total money generated in the concert

Since,

X+Y= 70

X= 70-Y

Substitute (70-Y) for X in equation 2

(70-Y)×10 + Y×12=804

700-10Y+12Y= 804

Collect the like terms

700+2Y=804

2Y=804-700

2Y= 104

Divide both sides by the coefficient of Y which is 2

2Y/2= 104/2

Y=52

Substitute 52 for Y in equation 1

X+Y=70

X+ 52=70

collect the like terms

X= 70-52

X=18

Hence the first type of ticket sold is 18 tickets and the second type of ticket sold is 52 tickets.

Answer:

x = -3.

Step-by-step explanation:

2x - 9 = 5x

2x - 5x = 9

-3x = 9

x = -3.

Answer:

3(6m) + m

first you multiply (you MUST do parentheses first) so 3*6 is 18 and you add the m in there is its 18m so then its:

18m + m

now you just add 18m + m which is 19m

answer: 19m

Answer:

1.3 miles = 82370 inches

Step-by-step explanation:

Formula: multiply the value in miles by the conversion factor '63360'.

So, 1.3 miles = 1.3 × 63360 = 82368 inches.

1.3 miles is equal to 82370 inches

We know that,

1 miles = 63360 inches,

To convert miles into inches, multiply the value in miles by the conversion factor '63360'.

1.3 miles = 1.3 × 63360 = 82368 inches.

Therefore, 1.3 miles = 82370 inches.

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The inequality that represents the cost, c, that Mr. Daniels can spend on the class trip is; c < 300

We are told that;

Mr. Daniels is organizing a class trip.

Mr. Daniels wants to spend less than $300

Thus, if the cost that Mr. Daniels can spend on the class trip is given as c, then it means that c has to be less than the amount which he wants to spend which is $300.

Thus, since c has to be less than $300, then it means that the inequality to be used would be a less than sign which can be expressed as;

c < 300

Thus, we conclude that it is the required inequality.

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Answer:

Step-by-step explanation:

I attached a picture below of what this situation looks like. As you can see, it is a right triangle problem. In order to solve for the speed of the boat, we first need to find out the difference between his distances when the angle is 60 and when it is 45. That's the same thing as finding x and y then subtracting. To find x:

\(sin60=\frac{200}x}\) so

x = 231 meters (I rounded to the nearest whole numbers in this problem.

To find y:

\(sin45=\frac{200}{231+y}\) so

\(y=\frac{200}{sin45}-231\) and

y = 52.

The distance between the angles 60 and 45 as 52 meters, and it took him 2 minutes to travel that 52 meters. Assuming that his rate doesn't change, he can travel 52/2 meters per minute, or 26 meters per minute.

Answer:

Step-by-step explanation:

A regular quadrilateral has 4 congruent sides and 4 angles

The ∛35 will be plotted between 3 and 4, but closer to 3 on the number line.

In basic mathematics, real numbers are shown as a fine graphic of a graduated straight line which is called a number line.

We know that 35 lies between 27 and 64 , and 27 = 3³ and 64 = 4³.

Hence the ∛35 will be plotted between 3 and 4 and since 35 is closer to 27 than 64 , therefore it will be closer to 3.

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Answer:

i think the 3rd one i have not done that in a while

Step-by-step explanation:

sorry if its not right

The graph shows the  inequality x² ≤ 16

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4.

Inequalities are often used to describe conditions or constraints in real-world problems.

You will notice that the values represented in the graph ranges from -4 to 4. Thus, solving x² ≤ 16 will produce these values. That is:

x² ≤ 16

x ≤ ±√16

x ≤ ±4

x ≤ -4 or x ≤ 4

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the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.

The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.

We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)

7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³

36 = (4/3)r³

27 = r³

r = 3  Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)

(dr/dt) = 7 / (4π(9))

(dr/dt) = 7 / (36π)

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Answer:

SA = 664 in.²

Step-by-step explanation:

Surface area of the rectangular prism = 2(LW + LH + WH)

Where,

Length (L) = 16 in.

Width (W) = 5 in.

Height (H) = 12 in.

Substitute the values

Surface area of the rectangular prism = 2(16*5 + 16*12 + 5*12)

= 2(80 + 192 + 60)

= 2(332)

= 664 in.²

Answer:

26 cards

Step-by-step explanation:

Sam:

⅓=2+6

=8

Bill:

3/3=3×8

=24

3/3=½

24+2=26

Now ,Min have 26 cards.

hope it help

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The equation of the regression line is y = 0.430x + 3.59.

A characteristic of the data that is ignored by the regression line is that: A. The data has a pattern that is not a straight line.

In order to determine a linear equation for the regression line (trend line) that models the data points contained in the table, we would have to use a graphing calculator (scatterplot).

In this scenario, the x-values would be plotted on the x-axis of the scatterplot while the y-values would be plotted on the y-axis of the scatterplot.

On the Excel worksheet, you should right click on any of the data point on the scatterplot, select format trend line, and then tick the box to display an equation for the regression line (trend line) on the scatter plot.

By critically observing the scatterplot (see attachment) which models the relationship between the x-values and y-values, a linear equation for the regression line (trend line) is given by:

y = 0.430x + 3.59

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Answer:

226.8 rounded to the nearest whole number is 227

Step-by-step explanation:

226 is farther away than 227 on a number line, so it rounds to 227.

Answer:

B

Step-by-step explanation:

The triangle RUS is similar to RST. 9/sqrt(90)=y/(3+x) and y^2=x^2+81. Solving all this will give x=27 and y=9*sqrt(10)

Value of x is 27 and value of y is \(9\sqrt{10}\).

The angle addition postulate in geometry states that if we place two or more angles side by side such that they share a common vertex and a common arm between each pair of angles, then the sum of those angles will be equal to the total sum of the resulting angle.

X-value:

<RST = \(90^{0}\)

\(tan( < RSU)= \frac{\overline R \overline U}{\overline S \overline U}\)

\(tan( < RSU) = \frac{3}{9}\)

\(< RSU = 18.435^{0}\)

Angle addition postulate:

<RST = <RSU + <TSU

\(90^{0} =18.435^{0} + < TSU\)

\(< TSU =71.565^{0}\)

\(tan( < TSU) = \frac{\overline T \overline U }{\overline S \overline U}\)

\(tan(71.565^{0})=\frac{x}{9}\)

\(x=27\)

Y-value:

<RST = \(90^{0}\)

\(tan( < RSU)= \frac{\overline R \overline U}{\overline S \overline U}\)

\(tan( < RSU) = \frac{3}{9}\)

\(< RSU = 18.435^{0}\)

Angle addition postulate:

<RST = <RSU + <TSU

\(90^{0} =18.435^{0} + < TSU\)

\(< TSU =71.565^{0}\)

\(cos( < TSU) = \frac{\overline S \overline U }{\overline S \overline T}\)

\(cos(71.565^{0})=\frac{9}{y}\)

\(y=9\sqrt{10}\)

Value of x is 27 and value of y is \(9\sqrt{10}\).

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The length of the base of the triangle is 16 m and the height of the triangle is 10 m

A polygon having three edges and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.Use the equation area = 1/2 * base * height to determine a triangle's surface area.

The basic Properties of a triangle :

The length of the base = b m

The height of the triangle = b - 6 m

The area of the triangle = 80 m²

Therefore,

(1/2)*b*(b-6) = 80

⇒ b² - 6b = 160

⇒ b² - 6b - 160 = 0

⇒b² - 16b + 10b - 160 = 0

⇒b(b-16) + 10(b- 16) = 0

⇒(b-16)(b =10) =0

The value of b = 16 and b = -10

The value of b is 16 as -10 is negetive and cannot be the length of the triangle.

The height of the triangle = b-6 = 10 m

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Answer:

1.)4(3x+2)-2

4*3x + 4*2 - 2

12x + 8 - 2

12x+6

2.)20b-16

4*5b - 4*4

4(5b-4)

The original cost of the tablet is $70.89 in the given algebraic equation.

A mathematical claim containing two equated algebraic expressions is known as an algebraic equation. When P and Q are polynomials, an algebraic equation has the general form P = 0 or P = Q. The term "multivariate equation" refers to an algebraic equation that has more than one variable.

Univariate equations are algebraic equations that only have one variable. Equations in algebra are balanced by definition. Due to this, the right and left sides of the equation will be equal.

Let the original cost be  x

then

15/100 = 24.99.x

x =  166.6

237.49 - 166.6

= $70.89

Thus, the original cost of the tablet is $70.89 in the given algebraic equations.

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Full question?

Lucas bought a tablet that was on sale at a 15% discount on your supra case for $24.99 which is been a total of $237.49. Write an equation to find the original cost of the tablet?

Answer:

clever

Step-by-step explanation:

21.5+28.5+27+13= 90%

10% of 400 prefer espresso

40 student

Answer:

40 students prefer the espresso flavor.

You can find this by adding all the other percents. Then take the number and subtract it from 100% or 1. Finally you multiply that number by the number of students to get your answer.

28.5+21.5+13+27 = 90%

100%-90% or 1 - .9 = .1

400 · .1 = 40 students

1. To calculate the percentage change in the price of a slice of pizza, we can use the midpoint formula:

Percentage change = [(New value - Old value) / ((New value + Old value) / 2)] * 100

Old value: $5 New value: $13

Percentage change = [($13 - $5) / (($13 + $5) / 2)] * 100 Percentage change = [(8) / (18 / 2)] * 100 Percentage change = (8 / 9) * 100 Percentage change = 88.89%

The percentage change in the price of a slice of pizza is approximately 88.89%.

2. To calculate the percentage change in the quantity of Sprite, we can use the same formula:

Old value: 15 cups New value: 17 cups

Percentage change = [(17 - 15) / ((17 + 15) / 2)] * 100 Percentage change = (2 / 16) * 100 Percentage change = 12.5%

The percentage change in the quantity of Sprite is 12.5%.

3. To calculate the Cross Price Elasticity of Demand, we use the formula:

Cross Price Elasticity = [(New quantity - Old quantity) / ((New quantity + Old quantity) / 2)] / [(New price - Old price) / ((New price + Old price) / 2)]

Old price of pizza: $5 New price of pizza: $13 Old quantity of Sprite: 15 cups New quantity of Sprite: 17 cups

Cross Price Elasticity = [(17 - 15) / ((17 + 15) / 2)] / [(13 - 5) / ((13 + 5) / 2)] Cross Price Elasticity = (2 / 16) / (8 / 9) Cross Price Elasticity = (2 / 16) * (9 / 8) Cross Price Elasticity = 0.28125

The Cross Price Elasticity of Demand is 0.28125.

4. Based on the positive percentage change in the price of a slice of pizza and the positive Cross Price Elasticity of Demand, we can conclude that Sprite and a slice of pizza are substitutes.

In summary:

The percentage change in the price of a slice of pizza is approximately 88.89%.

The percentage change in the quantity of Sprite is 12.5%.

The Cross Price Elasticity of Demand is 0.28125.

Sprite and a slice of pizza are substitutes.

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Answer:

5,859,375

Step-by-step explanation:

a10 = 3×5^9 = 3×1,953,125

= 5,859,375

Answer:

5,859,375

Step-by-step explanation:

Given :-

And we need to find out the 10th term of the sequence. Here firstly we should find the Common Ratio and then we can substitute the respective values in the formula to find the nth term of a geometric sequence .

Common Ratio :-

\(:\implies\) CR = 15 ÷ 3 = 5

The 10 th term :-

\(:\implies\) T_n = arⁿ - ¹

\(:\implies\) T_10 = 3 × 5 ¹⁰ - ¹

\(:\implies\) T_10 = 3 × 5⁹

\(:\implies\) T_10 = 3 × 1953125

\(:\implies\) T_10 = 5859375

Hence the 10th term is 5,859,375

Answer:

Step-by-step explanation:

the tip would be = 2.325 which rounds up to 2.33$ in total this would be17.83

You can approximate the probability using the standard normal distribution table by looking up the closest values for Φ(2) and Φ(1).

To calculate the probability P(1 < z < 2) for a standard normal random variable, we can use the cumulative distribution function (CDF) of the standard normal distribution.

The CDF gives us the probability that a standard normal random variable is less than or equal to a given value. We can use this information to calculate the probability between two values.

Let's denote the CDF of the standard normal distribution as Φ(z). The probability P(1 < z < 2) can be calculated as follows:

P(1 < z < 2) = Φ(2) - Φ(1)

To calculate this, we need to look up the values of Φ(2) and Φ(1) from a standard normal distribution table or use a calculator/computer software. However, since I don't have access to real-time computations in this environment, I am unable to provide the exact numerical value.

But you can use statistical software or online calculators to find the precise value. Alternatively, you can approximate the probability using the standard normal distribution table by looking up the closest values for Φ(2) and Φ(1).

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Answer:

i have made it in pic above